ONLY: An NPI-licenser and NPI-unlicenser Yimei Xiang, Harvard University Accepted for publication in Journal of Semantics. (DOI: 10.

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1 ONLY: An NPI-licenser and NPI-unlicenser Yimei Xiang, Harvard University Accepted for publication in Journal of Semantics. (DOI: /jos/ffx006) Abstract It is commonly argued that weak negative polarity items (NPIs) (e.g., any) can occur in any (Strawson) downward-entailing environment. This generalization, however, is challenged by Wagner s (2006) observations with the NPI-licenser only: although an only-clause is (Strawson) downward-entailing in its unfocused part, NPIs are not necessarily licensed there. In particular, DPonly does not license an NPI that appears within the unfocused part of its left argument (as seen in *Only a chair of any HUMANITIES F department met with the president), and VP-only does not license an NPI if this NPI and the focused item appear within the same island (as seen in *The president only met with a chair of any HUMANITIES F department). These observations suggest that the licensing status of an NPI in an only-sentence is not just determined by the polarity pattern of the environment where this NPI gets interpreted. To explain Wagner s (2006) observations, I argue that only is not just an NPI-licenser but also an NPI-unlicenser. Following Chierchia (2006, 2013), I assume that an NPI carries a domain feature [D] which activates domain alternatives, and that an NPI is unlicensed if exhaustifying its domain alternatives yields a contradiction. I further propose that only can check off the [D] feature of an NPI that appears within its syntactic argument. If the argument of only is downwardentailing with respect to an NPI, using only to check off the [D] feature of this NPI would return an inference that contradicts the prejacent presupposition and make this NPI unlicensed. In the case of VP-only association, if an NPI is not focused and doesn t appear within a focus-contained island, the contradiction can be avoided by F-movement. 1. Introduction Negative polarity items (henceforth NPIs), such as the emphatic expression any, are known to be licensed in downward-entailing (henceforth DE) environments (Fauconnier 1975, 1979; Ladusaw 1979). Prototypical DE environments are the following: (1) Under the semantic scope of negation a. John didn t read any papers. b. * John read any papers. (2) Within the scope of negative quantifiers a. Few/no/at most 3 students read any papers. b. * Many/most students read any papers. (3) In the left argument of universal quantifiers a. Every student who has read any papers passed the exam. b. * Every student who has read some papers passed any exams. 1

2 c. * Some student who has read any papers passed the exam. (4) In the antecedent of conditionals a. If John knows any big names, he will be invited. b. * If John is invited, he will know any big names. An environment is DE if and only if it supports downward inferences from a superset to a subset. For instance, observe the contrast between (5a) and (5b) that a downward inference holds from a term student to a more specific term smart student in the left argument of every, but not in the left argument of some. (5) a. Every student passed the exam. Every smart student passed the exam. b. Some students passed the exam. Some smart students passed the exam. Following von Fintel (1999) and Gajewski (2007), I define DE functions and DE environments as in (6), where the arrow stands for generalized entailment. 1 (6) a. Downward entailing functions A function f of type σ,τ is DE if and only if for all x and y of type σ such that x y, f(y) f(x). b. Downward entailing environments If α is of type δ and A is a constituent that contains α, then: A is DE with respect to α if and only if the function λx. A[α/v δ ] g[v δ x] is DE. [A[α/v] is the result of replacing α with a trace v in A.] 1 Generalized entailment is cross-categorically defined for items of any entailing type. Entailing types are defined recursively as in (1), adopted from Chierchia (2013: 204). Accordingly, t, e,t, e,et, and any type of the form... t are entailing types. (1) Entailing type a. t is a basic entailing type. b. If τ is an entailing type, then for any type σ, σ,τ is an entailing type. Following von Fintel (1999), I define generalized entailment as in (2). (2) Generalized entailment a. If φ, ψ are of type t, then: φ ψ if and only if φ is false or ψ is true. b. If β, γ are of an entailing type σ,τ, then: β γ if and only if for all α such that α is of type σ: β(α) γ(α). The basic case (2a) is defined based on truth values: a truth-value entails another if and only if it is not the case that the first is true and the second is false. In a generalized case, as schematized in (2b), a function entails another if and only if the result of applying the first function to any argument entails the result of applying the second function to the same argument. For example, smart student and student are functions of type e,t. smart student student, because for any x of type e, smart student (x) student (x). All the aforementioned cases can also be understood from a set-theoretic perspective: for any two sets A and B, A B if and only if A is a subset of B (written as A B ). 2

3 For example, the function λx. every A/A is B g[a x] is DE, and hence the sentence every A is B is DE with respect to A. The DE analysis of NPI-licensing can now be summarized as follows: (7) The DE analysis of NPI-licensing An NPI is grammatical if and only if it appears in a constituent that is DE with respect to this NPI. Nevertheless, the NPI-licensing effect of the exclusive focus particle only, first observed by Klima (1964), casts doubt on the DE analysis of NPI-licensing: while the NPI any is licensed in (8a) and (9a), these contexts do not seem to support downward inferences (Atlas 1993, 1996), as shown in (10a) and (10b), respectively. 2 In comparison, the ungrammaticality of (8b) and (9b) shows that the NPI any can be licensed by the overt exclusive particle only, but not by a covert exhaustifier. 3 (8) Right argument of DP-only a. Only JOHN F read any papers. b. * JOHN F read any papers. (9) Unfocused part under VP-only a. Mary only gave any books to JOHN F. b. * Mary gave any books to JOHN F. (10) a. Only JOHN F ate vegetables for breakfast. Only JOHN F ate kale for breakfast. b. Mary only gave fruit to JOHN F. Mary only gave apples to JOHN F. In responding to the NPI-licensing effect of only, many different positions have been defended in the literature, each of which weakens the strict DE condition to some extent for weak NPIs. For example, the Strawson-DE analysis grants the presuppositions of the consequence when a downward-inference is assessed (von Fintel 1999, Wagner 2006, Hsieh 2012). The grammatical view of NPI-licensing ignores presuppositions and implicatures when the meaning of a weak NPI is evaluated (Gajewski 2012, Chierchia 2013; see fn. 13). The pseudo-anti-additivity analysis (Atlas 1996) and the non-veridicality analysis (Giannakidou 2006) each use a weaker condition for the licensing of weak NPIs. It is further observed that the distributional pattern of NPIs in only-clauses is restricted by F- association: only cannot license an NPI that appears in its F-associate, as exemplified in (11). For simplicity, I call this fact Licensing Asymmetry. 2 Here and henceforth, CAPITAL letters mark stressed items, and the subscript F marks semantic focus. 3 The grammatical view of NPI-licensing (see section 3 and the references therein) assumes that focused items are always associated with overt or covert exhaustifiers. Accordingly, for example, the LF of (8b) contains a covert exhaustivity O-operator associated with the semantic focus JOHN F. Under this view, the contrast between (8a) and (8b) thus suggests that the covert O-operator cannot license NPIs. This contrast is expected by the grammatical view: the O-operator is non-monotonic; unlike only which asserts only an exhaustivity inference, the O-operator also asserts a prejacent inference. See more details in footnote 13. 3

4 (11) a. Only [some/*any students] F saw John. b. Mary only gave [some/*any books] F to John. Nevertheless, Drubig (1994) and Wagner (2006) observe that Licensing Asymmetry is not solely determined by F-association. In both examples in (12), only does not license the NPI any, although the F-associate of only is just the NP-complement of any. (12) a. Only [some/*any BOYS F ] arrived. b. John only read [some/*any PAPERS F ], (he didn t read any books). Similar facts are observed in (13) and (14). In these examples, only is associated with narrow focus, and the NPI any appears outside the focus: in (13), the NP-complement of any contains narrow focus; in (14), the anyp serves as an of -argument of the focused NP CHAIR; in (15), the anyp serves as the possessor of the focused NP ADVISOR. (13) a. Only a chair of [a/*any HUMANITIES F department] met with the president. b. The president only met with a chair of [a/*any HUMANITIES F department]. (14) a. Only [a CHAIR F of a/*any humanities department] met with the president. b. The president only met with [a CHAIR F of a/*any humanities department]. (15) a. Only [someone s/*anyone s ADVISOR F ] met with the president. b. The president only met with [someone s/*anyone s ADVISOR F ]. Examples (12) to (15) suggest two generalizations. First, DP-only does not license an NPI that appears within its left argument, regardless of whether this NPI is part of its associated focus. Second, VP-only does not license an NPI if this NPI and the focused item appear within the same island. In examples from (12) to (15), I used [ ] to enclose the minimal island that contains the semantic focus. 4 I call these facts uniformly Licensed-Nonfocal Mismatch, meaning that the part of an only-clause where an NPI can appear does not fully match up with the part that is not F-associated with only. 5 In sum, to capture the NPI-licensing effect of only, we need to answer at least three questions: 4 Determiner phrases like anyp can be considered islands, to the extent that the NP complement of a determiner cannot be moved out alone. According to Abels (2003), the complement of a phasal head such as the D head any cannot be moved by itself and strand its embedding phasal head, but must pied-pipe that phasal head. 5 There are some seeming counter-examples to this generalization. For example, the NPI any is licensed in (1a), although it appears within the left argument of DP-only. Interestingly, replacing the plural candidates with the singular existential indefinite a candidate makes any not licensed, as seen in (1b). Such a contrast is also observed with VP-only, as shown in (2). I thank Brian Buccola, Gary Thoms, and an anonymous reviewer for the observation. (1) a. Only [candidates with some/any relation to NY F ] met with the pope. b. Only [a candidate with some/*any relation to NY F ] met with the pope. (2) a. The pope only met with [candidates with some/any relation to NY F ]. b. The pope only met with [a candidate with some/*any relation to NY F ]. 4

5 (A) (B) (C) Only is not a prototypical DE-operator; why does it license NPIs? Why is it that the NPI-licensing effect of only is subject to Licensing Asymmetry? Why is it that Licensing Asymmetry is subject to Licensed-Nonfocal Mismatch? The rest of this paper is organized as follows. Section 2 and section 3 will review two representative theories on the NPI-licensing effect of only. One is the focus (F)-movement theory by Wagner (2006), and the other is the grammatical (G-)view of NPI-licensing by Chierchia (2006, 2013). I will show that both analyses have clear advantages but neither of them properly predicts the distributional pattern of NPIs under only. In section 4, I will propose a hybrid analysis that incorporates features of both theories. The main ingredients of the new analysis are the following: (A) (B) (C) Following the G-view of NPI-licensing, I assume that an NPI is licensed if and only if assessing its domain feature [D] does not yield a G-triviality. I argue that only is not only an NPI-licenser, but also an NPI-unlicenser : if an NPI is interpreted within the syntactic complement of only and if the prejacent of only is not downward-entailing with respect to this NPI, using only to assess the [D] feature of this NPI returns an inference contradicting the prejacent presupposition of only. In the case of VP-only association, the requirement of avoiding G-trivialities motivates F-movement. The semantic contradiction in (B) can be avoided if and only if the NPI is interpreted in the remnant VP. 2. The theory of F-movement and its shortcomings 2.1. The Strawson DE-condition To capture the NPI-licensing effect of only, von Fintel (1999) proposes a Strawson Downward Entailing (Strawson DE henceforth) analysis of NPI-licensing, as summarized in (16). Unlike the strict DE condition, the Strawson DE condition grants all presuppositions of the consequent sentence when the validity of a downward inference is assessed. (16) The Strawson DE analysis of NPI-licensing I argue that the licensing of any in (1a) and (2a) is irrelevant to only; instead, it correlates to the fact in (3) that an NPI can be licensed when it appears within a with-adjunct or a relative clause of a plural item. (3) a. (The) candidates with some/any relation to NY F met with the pope. b. A candidate with some/*any relation to NY F met with the pope. c. (The) candidates who had some/any relation to NY F met with the pope. d. A candidate who had some/*any relation to NY F met with the pope. 5

6 a. A function f of type σ,τ is Strawson DE if and only if for all x and y of type σ such that x y and f(x) is defined: f(y) f(x). b. An NPI is only grammatical if it is in the scope of a function f such that f is Strawson DE. Further, von Fintel (1999) argues that only+np is a Strawson DE function: only presupposes the truth of its propositional prejacent (Horn 1969); the scope of only+np is DE when the prejacent presupposition of only is satisfied, as shown in (17). (17) Kale is a vegetable. x y John ate kale for breakfast. f(x) is defined Only JOHN F ate vegetables for breakfast. f(y) Only JOHN F ate kale for breakfast f(x) 2.2. The theory of F-movement The Strawson DE condition, however, still cannot explain why VP-only association is subject to Licensing Asymmetry and why Licensing Asymmetry in general exhibits Licensed-Nonfocal Mismatch. In responding to these questions, Wagner (2006) proposes a theory of F-movement. This theory has components in both syntax and semantics, as outlined in the following The LF syntax of only First, both DP-only and VP-only have two syntactic arguments, a restrictor and a scope. In the case of DP-only, the restrictor and the scope correspond to its left argument and right argument, respectively. In the case of VP-only, F-association always invokes covert phrasal movement of the focused expression to the syntactic restrictor of only; thus the restrictor and the scope correspond to the F-moved phrase and the remnant VP, respectively. (18) a. DP-only b. VP-only Only JOHN F came. Mary only invited JOHN F. only JOHN F (restrictor) came (scope) only JOHN F (restrictor) λx (scope) VP Mary invited x Second, F-movement is island-sensitive (compare Anderson 1972, Jackendoff 1972, Rooth 1985); therefore, when only is associated into an island, the F-moved phrase ought to be the minimal island that contains the focus-associate of only (see also Drubig 1994). For instance, the F-moved item in (19a) ought to be the entire complex DP, and the one in (19b) ought to be the entire when-clause. 6

7 (19) a. Dr. Smith only rejected [the proposal that JOHN F submitted]. b. Dr. Smith only complains [when BILL F leaves the lights on] The semantics of only Wagner (2006) defines the lexical entry of only as in (20). Only is a two-place predicate; it asserts an exhaustivity inference and presupposes an existential premise. In (20), the arguments α and P correspond to the syntactic restrictor and the scope of only, respectively. The variable C stands for the exhaustification domain; its value is determined by both linguistic and contextual factors. (20) a. only (α)(p)= a C[P(a) ^P(α) ^ P(a)] b. Presupposition: x.p(x) Note that the presupposition (20b) is unconventional. It clearly differs from the standard prejacent presupposition (i.e., P(α)) assumed by Horn (1969). It is also weaker than the existential presupposition assumed by Horn (1996), which is generated by abstracting over the semantic focus, not the entire syntactic restrictor. See (21) for a simple comparison of these three presuppositions. Underlining marks the syntactic restrictor of only. (21) Only a female inhabitant of [Twin Earth] F met Particle Man. a. A female inhabitant of Twin Earth met Particle Man. Prejacent (Horn 1969) b. A female inhabitant from somewhere met Particle Man. Existential (Horn 1996) c. Someone met Particle Man. Existential (Wagner 2006) The main purpose for Wagner to weaken the presupposition of only is to capture the phenomenon of Licensed-Nonfocal Mismatch. If we assume the prejacent presupposition (21a), we would predict an unfocused part of the syntactic restrictor of only to be Strawson DE. Compare the following two lines of reasoning for illustration. In both lines of reasoning, the premise grants the prejacent inference of the consequent only-sentence. In (22), the downward inference from the focused NP student F to its subset [junior student] F does not hold, while in (23), the downward inference from the unfocused item inhabitant to its subset female inhabitant does hold. (22) A junior student is a student. x y A junior student met Particle Man. f(x) is defined Only a student F met Particle Man. f(y) Only a [junior student] F met Particle Man. f(x) (23) A female inhabitant is an inhabitant. x y A female inhabitant of Twin Earth met Particle Man. f(x) is defined Only an inhabitant of [Twin Earth] F met Particle Man. f(y) Only a female inhabitant of [Twin Earth] F met Particle Man f(x) 7

8 The same problem arises if we adopt Horn s (1996) existential presupposition (21b). For instance, in (24), if the premise grants the truth of this presupposition, a downward inference holds from the unfocused item inhabitant to its subset female inhabitant. (24) A female inhabitant is an inhabitant. x y A female inhabitant from somewhere met Particle Man. f(x) is defined Only an inhabitant of [Twin Earth] F met Particle Man. f(y) Only a female inhabitant of [Twin Earth] F met Particle Man f(x) Hence, if assuming that only triggers Horn s (1969) prejacent presupposition or Horn s (1996) existential presupposition, the Strawson DE analysis of NPI-licensing would predict that the unfocused part of the restrictor can license NPIs, contra fact in (25). (25) * Only any inhabitant of [Twin Earth] F met Particle Man. To solve this problem, Wagner assumes that only presuppose just a weak existential presupposition, which abstracts over the entire syntactic restrictor, and argues that the syntactic restrictor of only is not Strawson DE. For instance, in (26), the downward inference from the unfocused item inhabitant to female inhabitant seems to be invalid. (26) A female inhabitant is an inhabitant. x y Someone met Particle Man. f(x) is defined Only an inhabitant of [Twin Earth] F met Particle Man. f(y) Only a female inhabitant of [Twin Earth] F met Particle Man f(x) Motivating F-movement Wagner (2006) assumes that F-movement is triggered to strengthen the existential presupposition of only, in the spirit of the Maximize Presupposition (MP) Principle: (27) Maximize Presupposition Principle (Heim 1991) Out of two sentences which are presuppositional alternatives and which are contextually equivalent, the one with the stronger presuppositions must be used if its presuppositions are met in the context. This idea brings up Wagner s assumptions on syntax and semantics: F-movement minimizes the size the of the syntactic restrictor, which may have an effect on the strength of the statement that is grammatically encoded by the sentence. Consider the basic only-sentence in (28) for illustration. F-movement changes the size of the syntactic complement of only, as marked by underlining: the syntactic complement of only encloses the entire VP played BASKETBALL F in (28a) but just the semantics focus BASKETBALL F in (28b). Next, the existential presupposition triggered by only is obtained by abstracting over the entire VP in (28a), while over the focused noun phrase in (28b). Hence, the only-sentence obtains a stronger existential presupposition based on the F-moved form (28b). Finally, in the spirit of the MP Principle, the F-moved form is more preferable than the non-f-moved form. 8

9 (28) John only played BASKETBALL F. a. John only played BASKETBALL F. [Without F-movement] Presupposition: x. John x-ed. b. John only played BASKETBALL F. [With F-movement] Presupposition: x. John played x Consequences Wagner (2006) claims that the theory of F-movement is followed by two general restrictions on the NPI-licensing effect of VP-only, namely, the Island Restriction and the Head Restriction, as described in the following: (29) Head Restriction If only is associated with the head of a constituent, it does not license an NPI in the complement of the head. (30) Island Restriction Association with a constituent within an island cannot license an NPI that appears in the same island. The Head Restriction comes from the standard view that F-movement is phrasal movement: a head cannot take phrasal movement; therefore, when only is associated with a head, the F-moved item has to be the entire projection of this head. For instance, in (31), the F-moved element has to be the entire VP, including the anyp; therefore, the NPI any is interpreted within the syntactic restrictor of only and is not licensed. (31) * John only [CUT F any vegetables]. (Wagner 2006: 310) The Island Restriction follows Wagner s assumption that F-movement is sensitive to islands. For instance, in (32a), only is associated into the because-clause, which is an island; therefore, the F-moved item must be the entire because-clause, which contains an NPI any. In (32b), in contrast, the NPI anyone is outside the because-clause and therefore is not involved in F-movement. 6 (32) a. * Mary only gave a book to John [because BILL F gave any book to him]. b. She only gave anything to anyone [because YOU F did]. (Wagner 2006: 313) 6 The island effect of Licensing Asymmetry under VP-only might not be the real reason (or at least not the only reason) why the NPI any is not licensed in (32a). Chierchia (2013) indicates that because has an intervening effect on the licensing of NPIs. In (1b), even clause-mate negation cannot license the NPI anybody across because. (1) a. Mary doesn t believe that John criticized anybody. b. * Mary doesn t believe that John was arrested because he criticized anybody. 9

10 2.3. Problems with Wagner (2006) Wagner (2006) has convincingly argued that F-movement is needed for predicting the NPI-licensing effect of only, especially for unifying the Licensed-Nonfocal Mismatch behaviors of DP-only and VP-only. DP-only does not license an NPI that appears in its left argument, even if it is not associated with this NPI. Analogously, VP-only does not license an NPI if this NPI and the focused item appear within the same island, regardless of whether this NPI itself is focused. By virtue of F-movement, whatever explanation that works for DP-only will also work for VP-only. Nevertheless, Wagner s explanation of Licensed-Nonfocal Mismatch is infeasible: contrary to what he claims, with the weak existential presupposition (20b), an only-clause actually is Strawson DE with respect to any unfocused position (section 2.3.1). Moreover, in Wagner s account, the F-movement operation is not well-motivated or properly controlled (section and 2.3.3) Problems with Licensed-Nonfocal Mismatch Recall that Wagner weakens the presupposition of only, so as to avoid overly predicting an unfocused position in the syntactic restrictor of only to be Strawson DE. This attempt of eliminating Strawson DE-ness, however, is infeasible. The seeming failure of licensing a Strawson-downward inference in (26), repeated below, involves confusions between natural language semantics and meta-language interpretations. (33) A female inhabitant is an inhabitant. x y Someone met Particle Man. f(x) is defined Only an inhabitant of [Twin Earth] F met Particle Man. f(y)? Only a female inhabitant of [Twin Earth] F met Particle Man? f(x) To be more concrete, I suggest that the reason why the above reasoning is invalid is that the actual presupposition of the consequent only-sentence is stronger than what has been provided in the premise. The actual presupposition might be Horn s (1969) prejacent presupposition, Horn s (1996) existential presupposition, or Ippolito s (2008) conditional presupposition (see (42)), as described in the following: (34) Only a female inhabitant of [Twin Earth] F met Particle Man presupposes at least one of the following: a. A female inhabitant of Twin Earth met Particle Man. [Prejacent] b. A female inhabitant of some planet met Particle Man. [Regular existential] c. If a female inhabitant of some planet met Particle Man, then a female inhabitant of Twin Earth met Particle Man. [Conditional] To see whether Wagner s definition of only in (20) predicts an unfocused position of the restrictor to be Strawson DE, we should compare the predicted interpretations of the two only-sentences in (33), as shown in the following: (35) a. Only an inhabitant of [Twin Earth] F met Particle Man. 10

11 i. Assertion: If someone among C met PM, s/he is an inhabitant of TE. where C={an inhabitant of TE, an inhabitant of Earth, an inhabitant of Mars,...} ii. Presupposition: Someone met PM. b. Only a female inhabitant of [Twin Earth] F met Particle Man. i. Assertion: If someone among C met PM, s/he is a female inhabitant of TE. where C = {a female inhabitant of TE, a female inhabitant of Earth, a female inhabitant of Mars,...} ii. Presupposition: Someone met PM. From the interpretations above, we can see that Wagner s account actually predicts the sentence only an α of [Twin Earth] F met Particle Man to be Strawson DE as well as strictly DE with respect to α. It is Strawson DE because the downward inference holds in the asserted component (namely, (35a-i) entails (35b-i)). It is also strictly DE because (35a) and (35b) have exactly the same presupposition. Hence, Wagner cannot capture the phenomenon of Licensed-Nonfocal Mismatch in (25), no matter whether he follows the Strawson DE analysis or the DE analysis. This problem also extends to the case of VP-only association. As the interpretations in (36) show, using the definition of only in (20), Wagner would predict that the sentence John only CUT F x is Strawson DE as well as DE with respect to the object position x. It is Strawson DE because a downward inference holds in the asserted component (i.e., (36a-i) entails (36b-i)). It is also strictly DE because the two only-sentences, (36a) and (36b), have the same presupposition. 7 Hence, Wagner cannot predict the Head Restriction in (31). (36) a. John only CUT F vegetables. i. Assertion: If John did any action to vegetables, that action is no more than cutting. ii. Presupposition: John did something. b. John only CUT F kale. i. Assertion: If John did any action to kale, that action is no more than cutting. ii. Presupposition: John did something. In sum, the weak existential presupposition of only cannot help with explaining the phenomenon of Licensed-Nonfocal Mismatch. Wagner s account predicts that an only-clause is Strawson DE as well as DE with respect to any unfocused position Problems with the presupposition of only and why move? Recall that Wagner uses the MP Principle to motivate F-movement: the presupposition of only is obtained by abstracting the syntactic restrictor; F-movement reduces the size of the syntactic restrictor and hence strengthens the existential presupposition. In this section, I will show that 7 Wagner (2006: 310) himself writes the presupposition of (36b) as John did something with kale, which however conflicts with his main assumption that the existential import abstracts over the entire complement of only. 11

12 only triggers either a prejacent presupposition or a conditional presupposition, the involvement of which makes the MP-based analysis of motivating F-movement untenable. Wagner has noticed that the definition of only in (20) is too weak to account for sentences like (37), where only is associated with a conjunction. Intuitively, the sentence in (37) cannot be uttered if Sue invited only John, although the asserted exhaustivity inference in (37a) and the assumed existential presupposition in (37b) are both satisfied in this context. To predict this infelicity, Wagner adopts McCawley s (1993: 311) idea and proposes that the sentence (37) conversationally implies the prejacent inference in (37c). This implicature is derived roughly as follows. If the speaker believes that Sue didn t invite John or believes that Sue didn t invite Mary, she could have been more informative by leaving the person out of the list. Next, assuming the speaker is being cooperative in the Gricean sense and is well-informed, we conclude that the speaker believes that Sue invited both John and Mary. (37) Sue only invited [John and Mary] F. a. Assertion: Sue didn t invite anyone who is neither John nor Mary. b. Presupposition: Sue invited someone. c. Conversational implicature: Sue invited both John and Mary. As argued by Ippolito (2008: 59), however, the implicature analysis of the prejacent inference has at least two problems. First, it cannot explain why a negative only-sentence also introduces a prejacent inference, as in (38). If the speaker believes that Sue invited Mary but not John, saying Sue invited someone who is not John is less informative than the assumed exhaustive assertion Sue invited someone who is neither John nor Mary. Hence, we are not able to derive the expected prejacent inference of (38) based on the conversational maxims. (38) Sue not only invited [John and Mary] F Second, the implicature analysis cannot explain why the prejacent inference cannot be cancelled without an epistemic operator, as shown in (39). (39) a. # Only Mary can speak French in fact, not even she can. b. Only Mary can speak French, and maybe not even she can. Related to the second problem pointed out by Ippolito, the contrast between the following two conversations also suggests that the prejacent inference from only is more robust than an implicature from the weak scalar item some: unlike the scalar implicature from some, the prejacent inference affects the truth conditions of the only-clause and is much more difficult to cancel. (40) Did John invite some of the speakers to the dinner? a. Yes. Actually he invited all of them. b. # No. He invited all of them. (41) Did John only invite Mary? 12

13 a. # Yes. Actually he didn t invite anybody. b. No. He didn t invite anybody. Hence, the prejacent inference should not be treated as an independent implicature. Instead, we can analyze it as a presupposition (Horn 1969; Rooth 1985, 1992) or adopt Ippolito s (2008) analysis that the prejacent inference is a logical consequence of the scalar implicature (42a) together with a conditional presupposition (42b). (42) Only A is B. a. Implicature: Someone is B. (Derived by negating the stronger alternative No one is B.) b. Presupposition: If someone is B, A is B. c. A is B. In this section, I don t take a position as to which analysis correctly characterizes the presupposition(s) of only, but just show that the MP-based analysis of motivating F-movement is infeasible whichever analysis of presuppositions we follow. Under the presupposition analysis, the existential presupposition regardless of its strength is always entailed by and hence collapses under the prejacent presupposition, and thus the MP Principle cannot motivate F-movement. Alternatively, with Ippolito s (2008) conditional presupposition, the MP Principle would predict that the un-fmoved form is more preferable over the F-moved form: the existential inference is the antecedent of the conditional presupposition; therefore, strengthening the existential inference would weaken the presupposition. To be more concrete, consider the example (28) again, repeated below. If following Ippolito s (2008) analysis, we would have conditional presuppositions as follows. Observe that the presupposition in (43b) from the F-moved form is semantically weaker than the one in (43a) triggered in absence of F-movement. (43) John only played BASKETBALL F. a. John only played BASKETBALL F. [Without F-movement] Presupposition: If x [John x-ed], then John played basketball. b. John only played BASKETBALL F. [With F-movement] Presupposition: If x [John played x], then John played basketball Problems with when move? Wagner (2006) claims that F-movement is mandatory for VP-only association. I argue that this strong claim leads to two undesired consequences. First, it incorrectly predicts that an NPI associated with only is always unlicensed, even if this NPI appears under some other licenser. Recall that Wagner s assumptions yield the prediction that only does not license an NPI appearing inside the F-moved constituent. This prediction, together with the claim that F-movement is mandatory for VP-only association, implies a stricter constraint as follows: VP-only cannot be associated with any NPIs or with/into any NPI-contained islands 13

14 within which the NPIs are not licensed. This constraint, however, is too strong for cases like (44), where only is associated with an anyp across another NPI-licenser (i.e., clause-mate negation). (44) Mary only didn t give [any books] F to John. (She did her best to help him.) The stricter constraint predicts that the sentence (44) has to take the LF in (45). In this LF, however, the NPI any cannot be licensed: the anyp, as the minimal F-contained island, is moved to the syntactic restrictor of only, a context that is non-strawson DE and cannot license NPIs. 89 (45) only DP i any books VP Mary didn t gave t i to John Second, as pointed out by Büring and Sharvit and reported by Wagner (2006: fn. 20), assuming F-movement to be mandatory overly rules out possible interpretations for sentences like (46), where only is associated with a scopal element at most 3 students across another scopal element want. If F-movement were mandatory, the focused item would have to take only a wide scope reading. 8 Note that the NPI any is not licensed if only merely associates with any, as exemplified below. This is so because (1) doesn t have any excludable alternatives, failing to satisfy the additive presupposition of only. (1) How much books is such that Mary didn t give to John? *Mary only didn t give ANY F books to John. Consider the dialogue in (2) for illustration of the additive presupposition. The which-question with a restricted domain ensures that the exhaustification domain of only contains exactly three members, namely, I will invite John, I will invite Mary, and I will invite both John and Mary. The answer (2b) is infelicitous because the prejacent is the strongest one among the alternatives, which therefore makes the additive presupposition of only unsatisfied. In contrast, the answer (2c) is fully acceptable, because a covert exhaustification does not have an additive presupposition. (2) Which of John and Mary will you invite? a. Only JOHN F, (not Mary/ not both). b. # Only BOTH F. c. BOTH F. Likewise in (1), the exhaustification domain contains only propositions of the following two forms: (i) it is not the case that John read some paper in D (D D); (ii) it is not the case that John read most/all/... the papers in D. All of these alternatives are entailed by the prejacent and are not excludable. For more discussions on the additive presupposition, see Klinedinst (2005), Beaver and Clark (2009), among others. 9 An anonymous reviewer of Journal of Semantics points out the possibility of moving the entire negative VP complement to the restrictor of only. This movement is in general possible, but is disallowed under Wagner s framework: to enable this movement, we need to stipulate that the licensing of an NPI occurs prior to the satisfaction of the MP Principle; but Wagner assumes that the failure of licensing an NPI is due to F-movement, an operation motivated by the MP Principle. 14

15 (46) She only wanted to kiss [at most 3 students] F. To account for the correct scope readings, Wagner (2006: fn. 20) proposes that the F-moved item undergoes obligatory semantic or syntactic reconstruction. Nevertheless, if reconstruction were always feasible, then the focused anyp in (47) should also be reconstructed and licensed within the scope of VP-only, contra fact. (47) * Mary only wanted to read [any books] F. A defender of the reconstruction analysis might argue that only must be reconstructed in company with the F-moved phrase. Under this assumption, (47) would be interpreted as *Mary wanted to read only [any books] F. Nevertheless, this assumption is incorrect, because VP-only takes rigid scope reading (Taglicht & Randolph 1984, Rooth 1985, Bayer 1996), as exemplified in (48). (48) John is only required to meet MARY F. ( OK only > required; # required > only) 3. The G-view of exhaustifications 3.1. The G-view of scalar implicatures The grammatical (G-)view (Fox 2007, Chierchia et al. 2012, among others) was first introduced to analyze scalar implicatures. This view argues that the generation of scalar implicatures is not purely due to pragmatics (compare Grice 1975), given the fact that scalar implicatures can be generated in embedding contexts. The main ingredients of the G-view are summarized as follows. First, propositions with scalar items are associated with sets of alternatives, which are computed in the same way as answer sets of questions (Hamblin 1973) and alternative sets of focus (Rooth 1985, 1992, 1996). A recursive definition of alternative sets is schematized as follows: (49) Alternative sets a. For any lexical entry α, ALT(α)= i. { α } if α is lexical and does not belong to a scale; ii. { α 1,..., α n } if α is lexical and part of a scale α 1,..., α n ; Where ALT is a function from expressions to a set of interpretations. b. ALT(β(α))={b(a) : b ALT(β),a ALT(α)} Next, alternatives keep growing until factored into meaning via a covert exhaustivity operator O (or written as EXH ). This O-operator affirms the prejacent and negates all the alternatives that are not entailed by the prejacent, as schematized in (50). 10 The non-entailed alternatives are also called excludable alternatives. 10 In this formula, the propositional letter p is sloppily used as a syntactic expression in ALT(p). A stricter definition of the O-operator is as follows, where S is the sentential complement of O. 15

16 (50) O (p)=λw[p(w)=1 q ALT(p)[p q q(w)=0]] Accordingly, a scalar implicature is derived as a logical consequence of applying an O-operator over a sentence containing a scalar item. For instance, in (51), applying an O-operator over the bare some-sentence φ SOME affirms the prejacent φ SOME and negates the stronger scalar alternative φ ALL, yielding the scalar implicature φ ALL. (51) a. Some of the students came. Not all of the students came. b. ALT(φ SOME )={φ SOME,φ ALL } c. O(φ SOME )=φ SOME φ ALL 3.2. The G-view of NPI-licensing Chierchia (2006, 2013) extends the G-view to NPI-licensing with assumptions compatible with the strict DE condition. He proposes that the NPI any is an indefinite existential item like some but is lexically encoded with a grammatical feature [D]. This feature obligatorily activates a set of domain (D-)alternatives and must be checked off by a c-commanding O D -operator. Exercising an O D -operator over a sentence containing an occurrence of any has consequences in both syntax and semantics. In syntax, it checks off the [D] feature in the lexicon of any, just like a regular feature-checking operation. In semantics, it affirms the assertion of the prejacent and negates all the excludable D-alternatives, namely, the D-alternatives that are not entailed by the assertion of the prejacent. A schematic example for the total domain D and its corresponding D-alternative sets is given in (52). The D-alternative set includes the prejacent, while the proper D-alternative set does not. (52) a. Total-D:{a, b} Assertion = x {a, b} f(x) b. Sub-D: {a,b},{a},{b} D-ALT={ x {a,b} f(x), x {a} f(x), x {b} f(x)} c. Proper sub-d:{a},{b} Proper D-ALT ={ x {a} f(x), x {b} f(x)} Consider the basic positive sentence (53) to see how the G-view captures the DE condition of NPI-licensing. In LF (53a), an O D -operator is mandatorily present so as to check off the [D] feature of any D. The meaning of this LF proceeds as follows. First, the prejacent clause of O D (labeled S ) asserts an existential inference (53b) and is associated with a set of D-alternatives (53c). These D-alternatives are activated by the [D] feature of any D and are generated by substituting the total domain variable D with a subdomain D. Next, applying O D affirms the prejacent S and negates the excludable D-alternatives. Here, since the prejacent S is upward-entailing (henceforth UE) with respect to the domain variable D, the proper D-alternatives are all stronger than S and are all excludable. Hence, applying O D yields the exhaustivity inference in (53d). Crucially, the (1) O(S) =λ w[ S (w)=1 φ ALT(S)[ S φ φ(w)=0]] Note that this O-operator is distinct from the one used by Fox (2007), which negates only alternatives that can be negated consistently (viz., the so-called innocently excludable alternatives ). 16

17 exhaustivity inference in (53d) contradicts the prejacent inference S. 11 makes the sentence (53) ungrammatical and the NPI any unlicensed. Such a contradiction (53) * John read any papers. a. O D [ S John read any D papers] b. S = x D[P(x) R( j,x)] (John read some papers in the total domain D.) c. D-ALT(S)={ x D [P(x) R( j,x)] D D} d. D [D D x D [P(x) R( j,x)]] (for any proper subdomain D, John read no paper in D.) e. O D (S) = S (53d)= (# John read some papers in D, but for any proper subdomain D, he read no paper in D.) The contradiction in (53e) is in essence different from the one in (54). The former makes an utterance ungrammatical, while the latter makes an utterance infelicitous but not ungrammatical. (54) # It is raining and it isn t raining. To distinguish these two types of contradictions, Chierchia (2013: 49) adopts notions from Gajewski (2002) and describes the contradiction in (53e) as a Grammatical (G-)triviality. G-triviality is a special form of Logical (L-)triviality: L-trivialities are tautologies or contradictions in the traditional sense; G-triviality refers to a characteristic that a sentence receives the same truth value (true or false) regardless of how the lexical terminals in the structure are replaced. Compare the sentences in (55) for illustration. Expressions like John, smokes, and student are lexical terminals, and the rest are functional terminals. The contradiction in (55a) can be avoided by substituting the two occurrences of smoke with distinct lexical items (as in John smokes and doesn t dance.). In contrast, the meaning of (55b) is always contradictory no matter which lexical items are used. 12 Therefore, we identify (55a) as L-trivial, while (55b) as both L-trivial and G-trivial. 11 Consider the mini model in (1) for a simpler illustration of this idea. Assume that the total domain D contains exactly two items, paper p1 and paper p2. The D-alternative set is thus schematized as in (1b), consisting of three elements: the asserted proposition John read a paper in{p 1, p 2 } and two proper D-alternatives including John read a paper in {p1} and John read a paper in {p2}. The proper D-alternatives are not entailed by the assertion. Therefore, applying an O D -operator affirms the assertion and negates both proper D-alternatives, as schematized in (1c), yielding a contradictory inference that John read p 1 or p 2, and he did not read p 1, and he did not read p 2. (1) a. D={p 1, p 2 } b. D-ALT={R( j, p 1 ) R( j, p 2 ),R( j, p 1 ),R( j, p 2 )} c. R( j, p 1 ) R( j, p 2 ) R( j, p 1 ) R( j, p 2 )= 12 Following von Fintel (1993), Gajewski (2002) assumes the truth conditions in (1) for the logical skeleton of (55b), where the backslash \ stands for subtraction. These truth conditions say that {x} is the unique minimal set whose subtraction from the restrictor of the quantifier (i.e., P) makes the quantification true. 17

18 (55) a. # John smokes and doesn t smoke. [ x P and not P ] b. * Some student but John smokes. [ some P but x Q ] Next, Chierchia argues that the type of contradiction in (53e) can be avoided if the constituent that the O D -operator attaches to is DE with respect to the D variable of any D. Consider the basic negative sentence in (56) for instance. By virtue of negation, all the D-alternatives are entailed by the assertion and therefore not excludable. The O D -operator, although mandatorily present for the sake of feature checking, has no effect on semantics. (56) John didn t read any papers. a. O D [ S not [John read any D papers]] b. S = x D[P(x) R( j,x)] (John read no paper in the total domain D.) c. D-ALT(S)={ x D [P(x) R( j,x)] D D} d. O D (S) = S = x D[P(x) R( j,x)] (John read no paper in the total domain D.) 3.3. Extending the G-view of NPI-licensing to only Inspired by Krifka (1995) and Lahiri (1998), Chierchia (2006, 2013) extends the G-view of NPIlicensing to the licenser only. These approaches adopt the lexical entry of only from Horn (1969), namely, that only asserts an exhaustivity inference and presupposes the truth of its prejacent. The heart of this view is the following: the unfocused part of the asserted exhaustivity inference is DE and hence forms an NPI-licensing environment. Using Chierchia s (2013) schematic notations, we assume the LF in (57a). This LF contains two exhaustification operators, O D and only. In particular, O D checks off the [D] feature of the NPI any D, while only checks off the [F] feature of the focused item JOHN F. The prejacent presupposition and the asserted exhaustivity inference of the only-clause are schematized as in (57b) and (57c), respectively. The D-alternatives are generated from the assertion by replacing the total domain D with a subdomain D, as schematized in (57d). (57) Only JOHN F read any papers. (1) some P e,t but x e Q e,t = 1 if and only if a. some(p\{x})(q)= 1; b. S e,t [some(p\s)(q)=1 x S] Because some P Q is UE with respect to the restrictor P, condition (1a) entails condition (2). Nevertheless, because x, (2) contradicts condition (1b). Hence, any sentence of the form some P but x Q is a contradiction. (2) some(p\ )(Q) = 1, or equivalently, some(p)(q) = 1 For the purposes of this paper, it is enough to know that G-triviality is a type of L-triviality that affects grammaticality. 18

19 a. O D [ S only [JOHN F read any D papers ]] b. Presupposition of S: x D[P(x) R( j, x)] (John read some papers in the total domain D.) c. Assertion of S: λw. y D e [ x D[P w (x) R w (y,x)] y j] (For any individual y, if y read some papers in the total domain D, then y is John.) d. D-ALT(S)={ only [JOHN F read any D papers] : D D } ={λw. y D e [ x D [P w (x) R w (y,x)] y j] D D} The prejacent presupposition (57b), as argued by Gajewski (2011) and extended by Chierchia (2013), is irrelevant for assessing the [D] feature of the weak NPI any. 13 Moreover, the asserted 13 Gajewski (2011) proposes that presuppositions and implicatures are relevant only for the assessment of the [D] feature in strong NPIs. This proposal captures the contrast between weak NPI-licensing and strong NPI-licensing under only. For instance, in (1), only does not license the strong NPI in years. The prejacent presupposition of only is UE with respect to the D variable of in years. When the presupposition is accommodated, the entire only-clause is non-monotonic with respect to the D variable in the strong NPI in years. Then applying O D to assess the [D] features in the prejacent and the assertion yields a contradiction. See Chierchia (2013: section 4.4) for extensive discussion. (1) *Only JOHN came in years. a. John came in years. x[x came in years x j] b. John came in D. x[x came in D x j] where D YEARS This idea also explains the lack of NPI-licensing effect of the covert O-operator, as seen in (8b) and (9b). In the following, I show that both syntactically well-formed LFs of (2) yield a G-triviality. Under the LF in (2a), according to the definition of O in (50), the prejacent inference S is asserted by the covert O F -operator, as schematized in (2a-ii). Thus, when the O D -operator is applied, the prejacent inference will also enter into the assessment of the [D] feature, contrary to the case of the only-sentence (57). Crucially, the prejacent inference (the underlined part) and the exhaustivity inference (the rest) are UE and DE with respect to the NPI any, respectively; thus overall the complement of O D is non-monotonic with respect to the NPI any. Alternatively, under the LF in (2b), the [F] and [D] features will be checked off simultaneously, generating a set of alternatives via point-wise functional application (Hamblin 1973), as schematized in (2bii). Applying O affirms the prejacent and negates all the alternatives except the prejacent itself, yielding a contradiction. (2) * JOHN F read any papers. a. O D [O F [ S JOHN F,i read any D papers]] i. S =λ w. y D[P w (y) R w ( j,y)] (John read a paper in the total domain D.) ii. O F (S) =λ w. y D[P w (y) R w ( j,y)] x D e [ y D[P w (y) R w (x,y)] x j] (John and no one else read a paper in the total domain D.) iii. O D [O F (S)] = b. O D,F [ S JOHN F,i read any D papers] i. S =λ w. y D[P w (y) R w ( j,y)] ii. ALT(S)={λ w. y D [P w (y) R w (x,y)] D D,x D e } iii. O D,F (S) = 19